Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems to tackle problems that sit beyond the reach of automated tools — translating rigorous human arguments into machine-verifiable Lean proofs at the frontier of what formal verification can express.

This is a fully remote, flexible contract role designed for mathematicians who love precision, structural elegance, and the challenge of pushing proof assistants to their limits.

- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: Flexible hours, work on your own schedule

What You'll Do

- Translate informal mathematical proofs into Lean (and related proof systems) with a focus on clarity, correctness, and structure
- Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test and extend the limits of existing proof assistants — especially where automated tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more

Who You Are





- Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Have a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal proof system — Lean strongly preferred
- Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Able to take a dense, informal mathematical argument and express it in a form a machine can verify
- Comfortable working independently and asynchronously in a remote environment

Nice to Have

- Familiarity with type theory, the Curry–Howard correspondence, and proof automation tools
- Experience with large-scale formalization projects such as mathlib
- Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies to research collaborators

Why Join Us

- Work on cutting-edge AI research projects alongside leading AI labs and research teams
- Fully remote and adaptable — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually stimulating work
- Contribute directly to advancing AI reliability, formal reasoning, and high-integrity dataset creation
- Work at the true frontier of mathematics and computer science — on problems no automated tool can yet solve
- Potential for ongoing work and contract extension as new projects launch

📌 Mathematical Formalization Specialist (Canada)
🏢 Alignerr
📍 Canada